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Question

The number of solution(s) of the system of equations x+y=2π3 and cosx+cosy=32, where x and y are real, is

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Solution

We have cosx+cosy=32
2cos(x+y2)cos(xy2)=32
2cosπ3cos(xy2)=32 (using: x+y=2π3)
cos(xy2)=32, which is not possible.
Hence, the system of equaitons has no solution.

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